At equilibrium: H⁺, Ca²⁺, Mg²⁺, CO_2aq, H₂CO₃, HCO₃^-, CO₃^2-, OH^-

HAVE CHEMICAL EQUATIONS;WITH RULES: at 25°C

1. (01) H⁺+OH^-<=> H ₂ O ; K_w =[OH^-][H⁺]; K_w=10^-14
2. CO_2aq+H₂O<=> H₂CO ₃ ; K_a =[CO₂]/[H₂CO₃]; K_a=600
3. H₂CO₃<=> H⁺+HCO ₃ ^- ; K_b =[CO₃^2-][H⁺] /[H₂CO₃] ; K_b=2.5*10^-14
4. HCO₃^-<=>H⁺+CO ₃^2- ; K₂=[CO₃^2-][H ⁺]/[HCO₃^-] K₂=5.6*10^-11
5. Usual we know constant : K₁~ =[HCO ₃ ^-][H⁺] /[CO₂] K₁=4.3* 10^-7
   [HCO₃^-][H ⁺] / {[CO₂]+[H₂CO₃]} where [H₂CO₃]<<[CO₂]; K_a=600
6. System Electro neutrality: [2Ca²⁺]+[H⁺]= [OH^-]+[HCO₃^2-]+2[CO₃ ^2-]
   

Six equations, six values and nine components (please include '_aq' as water), quite too much for a model. Equation VI is the system restriction, independent equation for this system. We will use Mg2+ late in the discussion (remain eight components). Practically we will use two types of systems classification to simplify theoretical needs.

1. Closed system: whiteout material exchanges with other systems. With this classification "whiteout materials exchanges means another equation, at all seven equations and eight components. To have solution for this case we use computer to search the missing value from our system. We have to give the " if " value that will give the result and " else" value to prevent infinite cycle.
2. Open systems: with material exchanges. "With material exchanges" means in this case another equation and lucky the constant concentration of carbon dioxide in air. Is this concentration constant?

For closed systems, the low of mass preservation can be another restriction, according with the subject we will write:

• 7 . m_CO2=[CO₂]+[ HCO₃^-]+[CO₃ ^2-]

  Through definition alkalinity against methyl orange (the amount of carbonates, bicarbonates and alkali due to his exchange point at pH=3.4) have this mathematical form:

• 8 . m*10^-3=[OH^-]+2[CO₃ ^2-]+[H CO₃^--[H⁺]

  The Electro neutrality equation for entire system (Eq. VI), using equation (VIII) has another form:

• 9 . 2*10^-3m=[OH^-]+2[CO₃ ^2-]+[HCO₃^-] -[H⁺]